Abstract
This paper presents a new approach for enumerating all hydrogen bond arrangements of ice-like systems with periodic boundary conditions. It is founded on a topological procedure for the dimensional reduction and a new variant of the transfer matrix method based on small conditional transfer matrices. We consider a couple of new two-dimensional ice models on very unusual lattices. One of them is the twisted square ice model with crossing H-bonds. The other is the digonal-hexagonal model with double H-bonds. In spite of their uncommonness, these models are quite realistic, because from the standpoint of combinatorics and topology they are equivalent to the layers of usual hexagonal ice Ih under periodic boundary conditions in one of the directions. The exact proton configuration statistics for a number of 2D-expanded unit cells of hexagonal ice Ih and the residual entropy of the new ice models in the large system limit are presented.
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Acknowledgements
The author would like to thank Sotiris S. Xantheas of Pacific Northwest National Laboratory for assistance in the preparation of the manuscript. This study was supported in part by Interdisciplinary integration projects of Siberian Branch of the Russian Academy of Sciences, No 144.
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Kirov, M.V. New Two-Dimensional Ice Models. J Stat Phys 149, 865–877 (2012). https://doi.org/10.1007/s10955-012-0632-5
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DOI: https://doi.org/10.1007/s10955-012-0632-5